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Heterogeneous adaptive expectations and cobweb phenomena

Author

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  • Domenico Colucci

    () (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

  • Vincenzo Valori

    () (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

Abstract

We study a cobweb-type commodity market where n firms operate and characterised by a strictly monotone demand and supply. The firms are assumed to differ in a key parameter governing price expectations which we suppose to be adaptive. We characterise the unique steady state of the resulting economic dynamics in terms of stability and we study the impact of the number and diversity of firms: to this end we introduce the notions of structural and behavioural degree of instability which prove to be crucial in determining whether stability or instability prevail. We also consider the case of market merging and establish conditions to have stability (or instability) in the aggregated market in terms of the original (structural and behavioural) degrees of instability. We take up the issue of transitional dynamics and speed of convergence when the system is stable and characterise parametric configurations that maximise the speed of convergence. Motivated by the difficulty to actually observe expectations, whereas it is easier to measure some structural features of a given market, such as the relevant demand and supply price elasticities, we take the perspective of an observer (e.g. a policy maker) whose information set includes the structural but not the behavioural degree of instability. We therefore assume the firms - via the parameter which defines their expectations - are sampled independently from a population described by a given probability distribution. In this case the structural degree of instability determines how the number of potentially different firms affects the probability of ending up with a stable outcome. Analytical results are provided alongside numerical evidence.

Suggested Citation

  • Domenico Colucci & Vincenzo Valori, 2009. "Heterogeneous adaptive expectations and cobweb phenomena," Working Papers - Mathematical Economics 2009-01, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  • Handle: RePEc:flo:wpaper:2009-01
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    References listed on IDEAS

    as
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    3. William A. Branch, 2004. "The Theory of Rationally Heterogeneous Expectations: Evidence from Survey Data on Inflation Expectations," Economic Journal, Royal Economic Society, vol. 114(497), pages 592-621, July.
    4. Chiarella, Carl & He, Xue-Zhong & Hung, Hing & Zhu, Peiyuan, 2006. "An analysis of the cobweb model with boundedly rational heterogeneous producers," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 750-768, December.
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    16. repec:dau:papers:123456789/78 is not listed on IDEAS
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    More about this item

    Keywords

    heterogeneous agents; expectations; stability of steady states; market merging; speed of convergence;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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